Colloidal semiconductor Nanocrystals are the interest because of the control achieved in terms of composition, size and shape, making them a broad target of study and application devices.[1] Among the varieties of colloidal semiconductor nanocrystals, the nanoplatelets (NPLs) conveys several distinct properties, including the precisely controllable thickness, at the level of a few monolayers, which enables narrow emission line-widths, large exciton binding energies, large absorption cross sections and bright luminescence resulting for the giant oscillator strength effect [2-4].

Theoretical models have been developed to understand the underlying NPL electronic structure. In most cases, such models focus on neutral excitons [5-7], which are typically the dominant emitting species in colloidal nanocrystals. There is, however, increasing evidence that the emission spectrum of core-only and core/shell CdSe NPLs at low temperatures has a significant contribution from charged excitons (trions) [8-9]. Moreover, an increasing number of experimental works in the colloidal nanocrystal community are focusing on biexciton properties in NPLs, both in II-VI and halide perovskite materials[10-13].

Trions and biexcitons are of high technological interest for optoelectronic applications [8,9,14,15]. Understanding how the electronic structure of trions and biexcitons differs from that of excitons, and its dependence on the structural parameters of NPLs is of clear interest for further progress. In this work, we analyze how the presence of trions [16] and biexcitons in CdSe NPLs modifies the emission energy and oscillator strength as compared to neutral excitons. These properties are very sensitive to dielectric confinement and electronic correlations, which we describe accurately using the image-charge and variational Quantum Monte Carlo methods in effective mass Hamiltonians. Both, trions and biexcitons are red-shifted with respect to the exciton, and their emission and binding energy increases with increasing dielectric mismatch between the platelet and its surroundings, which is a consequence of the self-energy potential. In addition, the strong dielectric confinement enhances not only Coulomb attractions but also repulsions, which lowers the ratio of biexciton-to-exciton binding energy down to 0.07. Biexciton binding energy is less sensitive than exciton binding energy to lateral confinement, and yet it can reach values above 30 meV, thus granting room temperature stability. These results pave the way for rational design of excitons, trions and biexcitons species properties in metal chalcogenide nanoplatelets.